6.2 Trigonometric Functions: Unit Circle Approach/14: Difference between revisions
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<math>\left(\frac{ | <math>\left(\frac{1}{2}, -\frac{\sqrt{3}}{2}\right)</math> | ||
<math> | <math> | ||
\begin{align} | \begin{align} | ||
\sin{(t)} &= \frac{\sqrt{ | \sin{(t)} &= -\frac{\sqrt{3}}{2} & \csc{(t)} &= -\frac{2}{\sqrt{3}}\cdot\frac{\sqrt{3}}{\sqrt{3}}=\frac{2\sqrt{3}}{3}\\[2ex] | ||
\cos{(t)} &= \frac{ | \cos{(t)} &= \frac{1}{2} & \sec{(t)} &= \frac{2}{1} = 2\\[2ex] | ||
\tan{(t)} &= { | \tan{(t)} &= \frac{-\frac{\sqrt{3}}{2}}{\frac{1}{2}} = -\frac{\sqrt{3}}{2}\cdot\frac{2}{1} = -\sqrt{3} & \cot{(t)} &= -\frac{1}{\sqrt{3}}=-\frac{1}{\sqrt{3}}\cdot\frac{\sqrt{3}}{\sqrt{3}}=\frac{\sqrt{3}}{3} \\[2ex] | ||
\end{align} | \end{align} | ||
</math> | </math> | ||
Latest revision as of 22:19, 25 August 2022
![{\displaystyle {\begin{aligned}\sin {(t)}&=-{\frac {\sqrt {3}}{2}}&\csc {(t)}&=-{\frac {2}{\sqrt {3}}}\cdot {\frac {\sqrt {3}}{\sqrt {3}}}={\frac {2{\sqrt {3}}}{3}}\\[2ex]\cos {(t)}&={\frac {1}{2}}&\sec {(t)}&={\frac {2}{1}}=2\\[2ex]\tan {(t)}&={\frac {-{\frac {\sqrt {3}}{2}}}{\frac {1}{2}}}=-{\frac {\sqrt {3}}{2}}\cdot {\frac {2}{1}}=-{\sqrt {3}}&\cot {(t)}&=-{\frac {1}{\sqrt {3}}}=-{\frac {1}{\sqrt {3}}}\cdot {\frac {\sqrt {3}}{\sqrt {3}}}={\frac {\sqrt {3}}{3}}\\[2ex]\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/370eda479a2f0702b50a78e92a0eeccb821fd974)